To conclude, in this reply we have clarified that the Thakurta metric describes accreting BHs whose mass grows \(\propto a\)  and that must be accompanied by a smooth dark matter component which the BHs can accrete. Based on the arguments presented in [1]}, the required accretion rate is not realistic and, therefore, the Thakurta metric does not describe cosmological black holes. We did also show that the energy density of Thakurta PBHs is \(m a \, n_{\rm PBH}\)  instead of \(m n_{\rm PBH}\)  as claimed in [2]}.
